At first glance, this animal puzzle looks simple—but it requires careful algebra and attention to how the three weight combinations relate to one another.
We are given three animals:
- A dog
- A cat
- A mouse
The final picture asks us to calculate the combined weight of all three animals.
Let’s solve it step by step.
Step 1: Write Down the First Equation
The first scale shows a dog and a mouse weighing a total of 20 kg.
So we can write:
Dog + Mouse = 20 kg
Let:
- Dog = D
- Cat = C
- Mouse = M
The first equation becomes:
D + M = 20
Step 2: Write Down the Second Equation
The second scale shows a cat and a mouse weighing 10 kg.
Therefore:
Cat + Mouse = 10 kg
In algebraic form:
C + M = 10
Step 3: Write Down the Third Equation
The third scale shows a dog and a cat weighing 24 kg.
So:
Dog + Cat = 24 kg
In algebraic form:
D + C = 24
We now have three equations:
D + M = 20
C + M = 10
D + C = 24
Method 1: Add All Three Equations
The quickest way to solve this puzzle is to add all three equations together:
(D + M) + (C + M) + (D + C) = 20 + 10 + 24
Combine the values on the right:
20 + 10 + 24 = 54
Now look at the animals on the left:
- The dog appears twice.
- The cat appears twice.
- The mouse appears twice.
Therefore:
2D + 2C + 2M = 54
Factor out the number 2:
2(D + C + M) = 54
Divide both sides by 2:
D + C + M = 27
So the combined weight of the dog, cat, and mouse is:
✅ 27 kg
Method 2: Find Each Animal’s Individual Weight
We can also calculate the weight of every animal separately.
Start with:
D + M = 20
and:
C + M = 10
Subtract the second equation from the first:
D + M − (C + M) = 20 − 10
The mouse values cancel out:
D − C = 10
We already know:
D + C = 24
Now add these two equations:
D − C = 10
D + C = 24
Adding them gives:
2D = 34
Divide by 2:
D = 17
The dog weighs 17 kg.
Find the Cat’s Weight
We know:
D + C = 24
Substitute the dog’s weight:
17 + C = 24
Subtract 17:
C = 7
The cat weighs 7 kg.
Find the Mouse’s Weight
We know:
C + M = 10
Substitute the cat’s weight:
7 + M = 10
Subtract 7:
M = 3
The mouse weighs 3 kg.
Check the Calculations
Let’s verify every clue.
Dog and mouse:
17 + 3 = 20 kg ✅
Cat and mouse:
7 + 3 = 10 kg ✅
Dog and cat:
17 + 7 = 24 kg ✅
Everything matches perfectly.
Now add all three animals:
17 + 7 + 3 = 27 kg
🎯 Final Answer
The dog weighs 17 kg, the cat weighs 7 kg, and the mouse weighs 3 kg.
Therefore:
🐶 + 🐱 + 🐭 = 27 kg
Did you solve it before reading the answer? Share your result in the comments and challenge your friends!
